Relativistic Tidal Interaction of Stars with a Rotating Black Hole

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Abstract
The tidal interaction of n = 1.5 polytropic stars with a massive rotating black hole is studied numerically. The general relativistic tidal potential for the Kerr metric is used to evaluate tidal forces exerted on a star. The hydrodynamic response of a star to these forces is treated in the Newtonian approximation using a three-dimensional, Eulerian, PPM hydrodynamical code. We compute the energy, ΔE, and angular momentum, ΔL, transferred into a star and the mass, ΔM, lost by the star during the interaction. The quantities ΔE, ΔL, and ΔM depend on the stellar orbit, stellar structure, and the black hole's mass and angular momentum in a complicated way. We show that the dependence can be factorized by introducing a single dimensionless parameter Ċ proportional to the integral of the square of the trace of the tidal tensor along the stellar trajectory. The energy and angular momentum transfer, and the mass loss as functions of Ċ are found in hydrodynamical simulations. Analytical approximations to ΔE(Ċ) and ΔM(Ċ) are constructed. The value of Ċ does not depend on the stellar structure. It is a universal function on the parameters of the orbit and can tabulated once and for all. Tables of Ċ are presented. The results of this paper allow one to easily determine the outcome of tidal interaction for every possible combination of the input parameters. We find that the final energy of a star or a stellar remnant (if mass is lost) and its internal angular momentum as well depend most strongly on the angle between the initial orbital angular momentum and the angular momentum of the black hole.

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